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An application of H-differentiability to nonnegative and unrestricted generalized complementarity problems

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2008年第1期39卷 51-74页

作者： Tawhid, M. A. Thompson Rivers Univ Sch Adv Technol & Math Dept Math & Stat Kamloops BC V2C 5N3 Canada

This paper deals with nonnegative nonsmooth generalized complementarity problem, denoted by GCP(f,g). Starting with H-differentiable functions f and g, we describe H-differentials of some GCP functions and their merit functions. We show how, under appropriate conditions on H-differentials of f and g, minimizing a merit function corresponding to f and g leads to a solution of the generalized complementarity problem. Moreover, we generalize the concepts of monotonicity, P (0)-property and their variants for functions and use them to establish some conditions to get a solution for generalized complementarity problem. Our results are generalizations of such results for nonlinear complementarity problem when the underlying functions are C-1, semismooth, and locally Lipschitzian.

关键词： H-differentiability semismooth-functions locally Lipschitzian generalized Jacobian generalized complementarity problem GCP function merit function regularity conditions

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On minimizing some merit functions for nonlinear complementarity problems under H-differentiability

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2008年第1期139卷 127-140页

作者： Tawhid, M. A. Goffin, J. L. Thompson Rivers Univ Sch Adv Technol & Math Dept Math & Stat Kamloops BC V2C 5N3 Canada McGill Univ Fac Management Montreal PQ H3A 1G5 Canada

In this paper, we describe the H-differentials of some well known NCP functions and their merit functions. We show how, under appropriate conditions on an H-differential of f, minimizing a merit function corresponding to f leads to a solution of the nonlinear complementarity problem. Our results give a unified treatment of such results for C(1)-functions, semismooth-functions, and locally Lipschitzian functions. Illustrations are given to show the usefulness of our results. We present also a result on the global convergence of a derivative-free descent algorithm for solving the nonlinear complementarity problem.

关键词： H-differentiability semismooth-functions locally Lipschitzian functions nonlinear complementarity problems NCP functions merit function descent algorithms

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On minimizing the implicit Lagrangian for nonlinear complementarity problems under H-differentiability

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APPLIED MATHEMATICS AND COMPUTATION 2007年第1期185卷 484-491页

作者： Tawhid, M. A. Thompson Rivers Univ Sch Adv Technol & Math Dept Math & Stat Kamloops BC V2C 5N3 Canada

In this paper, we describe H-differential of the implicit Lagrangian function. We show how, under appropriate regularity conditions on an H-differential off, minimizing the implicit Lagrangian function corresponding to f leads to a solution of the nonlinear complementarity problem. Our results give a unified treatment of such results for C-1-functions and for locally Lipschitzian functions. (c) 2006 Elsevier Inc. All rights reserved.

关键词： H-differentiability semismooth-functions locally lipschitzian generalized jacobian nonlinear complementarity problem NCP function merit function regularity conditions

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